# Abiogenesis – the bar

Abiogenesis gets a lot of stick from sceptics because it seems intuitively wrong. In my experience, the most common problem people seem to have with the idea is that it appears to rely on a highly complicated chemistry arising from nothing more than random processes. While there isn’t yet a conclusive empirical description of how this may have occurred, there is work in the area, and it doesn’t seem to be in any way in violation of the physics and chemistry we know today.

Disclosure: I totally buy abiogenesis. I think it’s not even slightly implausible. I have seen order come from chaos in a number of cases, not least in an evolution demonstration I wrote for fun last year. This in no way violates the 2nd Law of Thermodynamics, in the same way that tidying cutlery in a drawer doesn’t.

There’s also a point to be made that supernatural hypotheses, such as the Christian creation myth, are also examples of abiogenesis, but that’s nitpicking, and I won’t talk about that here.

One thing that I do credit sceptics with, is that they have a point about probability. I think they don’t have the point they believe they have though. Typically the trope goes like this, “the probability of a fully-formed protein (or even in some cases, a working cell!) emerging from a bunch of atoms is astronomically low, therefore, it didn’t happen”. My thoughts on this idea are:

1. Because of the continuing work into the subject, and the lack of information from the development of life, I think we don’t know how to tell the probability of a self-replicating molecule forming that could kick-start the process of evolution.
2. The probability of a replicator developing doesn’t need to be high to start life, because it only has to happen once.

This second point is the crux of this post. What would be an acceptable probability for abiogenesis to be a 95% probable explanation for life on Earth? I think this could be very low.

# Challenge

I wonder what the probability of abiogenesis in a given litre of reactive substrate would have to be to produce a 95% likelihood of development of life in our galaxy.

# Drake equation

Let’s borrow some values from the Drake equation to get some ballpark numbers to estimate locations where life could develop.

 Symbol Meaning Current Value $f_{p}$ Fraction of stars that have planets $1$ $n_{e}$ Average number of satellites suitable for life $0.4$

Let’s add to that some more numbers:

 $n$ Number of stars in the galaxy $100000000000$ $V$ Average volume of liquid water available for chemistry (cubic km) $1386000000$

I took $n$ from the Drake equation current values, and $V$ from here, assuming that Earth has a typical value.

So that gives us an available volume of:

$n \times f_{p} \times n_{e} \times V \times 10^{12}$ litres

Now we need to know how long this was able to react. Let’s take an educated guess from Universe Today, and pretend the early universe was too violent for life formation until the galactic disk had formed. That gives us 10 billion years to play with:

 $T$ Duration of life development (billion years) $10$ $A$ Age of developed life (billion years) $3$ $P$ Probability abiogenesis will occur in the galaxy in the available time $0.95$ $P_{a}$ Probability abiogenesis will occur in 1 litre of substrate in 1 year $?$

This gives:

$P_{a}=\frac{P}{((T - A) \times 10^{9} \times n \times f_{p} \times n_{e} \times V \times 10^{12})}$

So:

$P_{a}=\frac{0.95}{((10 - 3) \times 10^{9} \times 10^{11} \times 1 \times 0.4 \times 1.386 \times 10^{9} \times 10^{11}}$

Which is very very small. Very small.

$2.4 \times 10^{-42}$

On average, then. If abiogenesis is rare enough that it only happened once in our galaxy with a confidence of 95%, and a lab scientist was performing an experiment with the right experimental conditions on 1 litre of substrate, she would have to wait about 3000 billion billion billion times the age of the universe so far. On average! If she were unlucky, perhaps she’d have to wait longer…